Observations on the discount rate

The change from 6 per cent to 3.5 per cent for the standard rate to be used (dictated by HM Treasury in April 2004) effectively puts a higher weight on future costs, with the aim of encouraging longer-term, more sustainable, development.

The choice of the discount rate (interest rate) used can have a dramatic effect on the outcome of the analysis. As an example, an annual energy bill of £100,000 over 30 years will have a present value of around £1.84 million if a 3.5 per cent interest is taken, but only £656,600 at 15 per cent.

Corporation, to evaluate contractors’ bids. Thus, if a contractor’s overall lump sum was low but they required a greater proportion of payment in year 1, this would be reflected in the NPV calculation.

The UK Government’s recommended discount rate is 3.5 per cent (Green Book). Calculating the present value of differences between the stream of costs and benefits provides the net present value (NPV) of an option. The NPV is the primary criterion for deciding whether government action can be justified (HM Treasury, 2003).

Annual equivalent This is the total of:

• any regular annual payments and income, such as wages, rents, etc; • annual interest on items of capital expenditure;

• a sinking fund, the amount which would have to be put away annually to repay the capital cost at the end of the period.

Alternatively, the annual interest and sinking fund can be combined and expressed as the annual instalments which would be required to pay off the capital costs and interest over the term of years in question (rather like paying off a loan for a house through a mortgage).

Both of these methods will give a similar answer, and which one is used is purely a matter of convenience and depends on whether you are thinking in terms of capital finance or in terms of annual income and expenditure.

9.5 Calculations

In the following formulae n represents the number of years and i is the interest rate expressed as a decimal fraction of the principal, e.g. 5 per cent = 0.05.

The following standard time value of money tables should be downloaded from the internet. Table 1 – Present Value Factors

Table 2 – Present Value of Annuity Factors.

Formula 1 – Compound interest = (1 + i)n

If a sum of money is invested for some years it will have earned some interest by the end of the first year. Compound interest assumes that this earned money is immediately added to the principal and reinvested on the same terms, this process being repeated annually.

What will be the value of £5,500 invested at 9 per cent compound interest for 5 years? Formula (1+i)5_{shows that £1 so invested will grow to £1.54.}

£5,500 will grow to £5,500 x 1.54 = £8,470.

Formula 2 – Present value of £1 = 1/ (1 + i)n

In the compound interest example, £5,500 invested for 5 years at 9 per cent grew to £8,470. The converse of this is that the present value of £8,470 in 5 years’ time at 9 per cent interest is £5,500; i.e. the amount that will grow to that sum at the end of 5 years.

What is the present value of £1,200 in 35 years’ time discounted at 10 per cent per annum? By the use of the formula, the present value of £1 in such circumstances is 0.0356 (refer to 142 Whole-life costing

Table 1 – Present Value Factors). The present value of £1,200 is therefore 1,200 x 0.0356 = £42.72.

Formula 3 – Present value of £1 payable at regular intervals [(1+i)n_{– 1]/[i (1 + i)}n_]

This formula shows the present value of future regular periodic payments or receipts over a limited term of years. It is, therefore, very useful for assessing the capital equivalent of things like running costs, wages or rents.

What is the present value of £1,200 payable annually for 10 years, assuming an interest rate of 8 per cent per annum?

Example

It is desired to compare the whole-life costs of two types of windows for an office building, whose life is intended to be 40 years. The rate of interest allowed is 3 per cent per annum compound.

Whole-life costs of Windows Type A

Windows Type A will cost £900,000, will require redecorating every 5 years at a cost of £20,000 and will require renewing after 20 years at a cost of £1,200,000.

£

Initial cost 900,000

Present value at 3 per cent of:

Redecoration after 5 years: £20,000 @ 0.8626 (PV of £1) 17,252 Redecoration after 10 years: £20,000 @ 0.7441 14,882 Redecoration after 15 years: £20,000 @ 0.6419 12,838

Renewal after 20 years: £1,200,000 @ 0.5537 664,440

Redecoration after 25 years: £20,000 @ 0.4776 9,552

Redecoration after 30 years: £20,000 @ 0.4120 8,240

Redecoration after 35 years: £20,000 @ 0.3554 7,108

--- £1,634,312 =========

Whole-life costs of windows Type B

Windows Type B will cost £1,250,000 and will last the life of the building without any maintenance, although a sum of £300,000 is to be allowed for general repairs after 20 years.

£

Initial cost 1,250,000

Present value at 3 per cent of:

Repairs after 20 years: £300,000 @ 0.5537 166,110

--- £1,416,110 =========

Saving by using Windows B is therefore £1,634,312 minus £1,416,110 = £218,202. It would therefore appear to be justifiable to use the initially more expensive Windows Type B, as this will prove much the cheaper in the long run.

Inflation

The discount rate is not the inflation rate but is the investment premium over and above inflation. Provided inflation for all costs is approximately equal, it is normal practice to exclude inflation effects when undertaking Life-Cycle Cost analysis (HM Treasury, 2003). In recent years inflation in the UK has been 2–4 per cent per annum; however, 15 years ago it was in double figures and in the early 1970s, following the Middle East crisis, it was over 25 per cent per annum.

The solution to the example above did not take into account inflation. If the original windows were worked out on the basis of 10 per cent annual inflation and 13 per cent interest we would get much the same result as with no inflation and interest at 3 per cent.

9.6 Problems with assessing whole-life costs

We have seen how whole-life costing enables us to consider the long-term implications of a decision and provides a way of showing the cost consequences. It has been identified by Ferry et al. (1999) that there are a number of potential fundamental problems in using a whole-life costing approach such as the following:

1 Initial and running costs cannot really be equated:

• The maintenance charges will fall upon the purchaser not on the developer.

• Even with public buildings, e.g. schools, the bulk of the construction costs are paid for by one authority, with another authority responsible for maintenance.

• Money for capital developments is often more difficult to find than money for current expenditure.

2 The future cannot really be forecast:

• The cost of maintenance is pure guesswork.

• The amount of money spent on decoration and upkeep is determined more by the body responsible for maintenance, e.g. new owners, than by any quality inherent in the materials.

• Hard-wearing materials may give an old-fashioned appearance and may be replaced before they are life expired.

• Major expenditure on repairs is usually caused by unforeseen failure of detailing, faulty material or poor workmanship and is almost impossible to forecast.

• Interest rates cannot be forecast with any certainty, particularly over long periods. Would you like to guess what the Bank of England (or the European Bank) would do in say 20 years?

Whilst these comments reflect genuine concerns, they have not in any significant way undermined the value of WLC, which is still widely used particularly in the evaluation of PFI schemes. However, it is useful to be aware of these potential limitations of WLC.

The National Audit Office Report, Improving Public Services through Better Construction (NAO, 2005), also identified four key barriers to successful whole-life costing. First, the lack of clarity on what is meant by whole-life costing. Second, a lack of robust historical data on running costs. Third, people making investment decisions need a tool not just based on cost but other drivers 144 Whole-life costing

such as time, sustainability, quality and return on investment. The calculations are done in a vacuum and there is no way of comparing and evaluating the options. Finally, there is a lack of tangible evidence of the benefits of whole-life costing (Green, 2005). It is significant to note in the 2011 report of the NAO on Lessons from PFI and Other Projects that the issue of unreliable historical data on running and maintenance costs did not escape notice, being cited as a weakness in some departments’ (e.g. Highways Agency) evaluation of PFI projects (NAO, 2011). In the Highways Agency’s case, substantially lower costs were quoted by the PFI bidders for operations and maintenance, raising significant concerns about the agency’s cost estimates.

In an effort to address some of these issues, the Building Cost Information Service (BCIS) has developed a standardized approach to whole-life costing. In 2007, BCIS launched BCIS Occupancy Online. Initially this service would provide information at the building level based on the estimates of maintenance and occupancy across a range of building types, and a profile for that expenditure based on the BMI occupancy cost plans. The user would be able to change the time period and the inflation or discount rate and adjust the costs for time and location to provide cash flow, at current or future prices and net present value (Martin, 2007). In 2008 an international standard BS ISO 15686-5:2008: Buildings and Constructed Assets, Service Life Planning – Life-cycle costing was introduced.

Although this provided a set of principles enabling practitioners to produce consistent life- cycle costing analysis, it did not provide the UK guidance that was needed. So a working group was set up to produce guidance to the standard. This is called the standardised method of life-cycle costing (SMLCC) for construction procurement.

(Martin, 2008: 76) In his article in Building magazine, Joe Martin of the BCIS includes a budget life-cycle case study for a 1,000-capacity secondary school with a 30-year period of analysis showing construction costs of £16.3 million (43 per cent of total life-cycle costs), maintenance costs of £7.3 million (19 per cent of total life-cycle costs) and operation costs of £14.7 million (38 per cent of total life-cycle costs).

9.7 Whole-life value

Increasingly, major procurement in the public and private sector is being undertaken on the basis of not just lowest capital, or even whole-life costs, but value (Bourke et al., 2005). Whole-life value (WLV) encompasses economic, social and environmental aspects associated with the design, construction, operation, decommissioning and, where appropriate, reuse of the asset or its constituent materials at the end of its useful life.

An important part of whole-life costing is compiling the life-cycle assessment (LCA). This is a systematic set of procedures for compiling and examining the inputs and outputs of materials and energy and the associated environmental impacts directly attributable to the functioning of a product or service system throughout its life cycle.

However whole-life value includes more than whole-life costing or life-cycle assessments, which are integral to the process. The application of WLV includes the consideration of the perceived costs and benefits of some or all of the stakeholders’ relevant value drivers. The key techniques that are integral to WLV evaluations of building and infrastructure projects include:

• Whole-life costing and life-cycle assessment: WLC deals primarily with financial costs, whereas LCA deals primarily with environmental impacts.

• Multi-criteria analysis: MCA is used in conjunction with both WLC and LCA to evaluate alternative options based on criteria developed with stakeholders.

• Group decision-making processes: these processes include value management and risk management to engage stakeholders in the WLV process.

146 Whole-life costing